There's a graveyard of 100s of papers with "approximate near linear time attention." They always hope the speed increase makes up for the lower quality, but it never does. The quadratic time seems inherent to the problem. Indeed, there are lower bounds showing that sub n^2 algorithms can't work: https://arxiv.org/pdf/2302.13214
Attention at Constant Cost per Token via Symmetry-Aware Taylor Approximation
21–30 of 104 posts
Re: Attention at Constant Cost per Token via Symmetry-Aware Taylor Approximation
#22There's a graveyard of 100s of papers with "approximate near linear time attention." They always hope the speed increase makes up for the lower quality, but it never does. The quadratic time seems inherent to the problem. Indeed, there are lower bounds showing that sub n^2 algorithms can't work: https://arxiv.org/pdf/2302.13214
Dumb question: is the quadratic time complexity for training, inference, or both?
Re: Attention at Constant Cost per Token via Symmetry-Aware Taylor Approximation
#23Re: Attention at Constant Cost per Token via Symmetry-Aware Taylor Approximation
#24There's a graveyard of 100s of papers with "approximate near linear time attention." They always hope the speed increase makes up for the lower quality, but it never does. The quadratic time seems inherent to the problem. Indeed, there are lower bounds showing that sub n^2 algorithms can't work: https://arxiv.org/pdf/2302.13214
I think DeepSeek V3.2 is sub n^2, but it clearly performs quite well, refuting the alleged lower bounds in the paper.
Re: Attention at Constant Cost per Token via Symmetry-Aware Taylor Approximation
#25There's a graveyard of 100s of papers with "approximate near linear time attention." They always hope the speed increase makes up for the lower quality, but it never does. The quadratic time seems inherent to the problem. Indeed, there are lower bounds showing that sub n^2 algorithms can't work: https://arxiv.org/pdf/2302.13214
I think DeepSeek V3.2 is sub n^2, but it clearly performs quite well, refuting the alleged lower bounds in the paper.
> DSA reduces the core attention complexity of the main model from O(L^2) to O(Lk), where k ([1] https://arxiv.org/pdf/2512.02556
Re: Attention at Constant Cost per Token via Symmetry-Aware Taylor Approximation
#26There's a graveyard of 100s of papers with "approximate near linear time attention." They always hope the speed increase makes up for the lower quality, but it never does. The quadratic time seems inherent to the problem. Indeed, there are lower bounds showing that sub n^2 algorithms can't work: https://arxiv.org/pdf/2302.13214
This paper at least aspires to reproduce 'true' attention, which distinguishes it from many of the others. TBD if its successful in that.
Re: Attention at Constant Cost per Token via Symmetry-Aware Taylor Approximation
#27There's a graveyard of 100s of papers with "approximate near linear time attention." They always hope the speed increase makes up for the lower quality, but it never does. The quadratic time seems inherent to the problem. Indeed, there are lower bounds showing that sub n^2 algorithms can't work: https://arxiv.org/pdf/2302.13214
[1] Attention Is Not What You Need, https://arxiv.org/abs/2512.19428
Re: Attention at Constant Cost per Token via Symmetry-Aware Taylor Approximation
#28There's a graveyard of 100s of papers with "approximate near linear time attention." They always hope the speed increase makes up for the lower quality, but it never does. The quadratic time seems inherent to the problem. Indeed, there are lower bounds showing that sub n^2 algorithms can't work: https://arxiv.org/pdf/2302.13214
> self-attention is efficiently computable to arbitrary precision with constant cost per token This paper at least aspires to reproduce 'true' attention, which distinguishes it from many of the others. TBD if its successful in that.
Re: Attention at Constant Cost per Token via Symmetry-Aware Taylor Approximation
#29Earlier quoted context omitted.
> this is where the taylor expression would fail to represent the values well. "In practice, we find that four Taylor terms (P = 4) suffice for recovering conventional attention with elementwise errors of approximately the same magnitude as Float16 resolution"
I read that too, but I wondered whether elementwise error is the right metric. Surely the actual error metric should be to evaluate model performance for a conventional transformer model and then the same model with the attention mechanism replaced by this 4th order Taylor approximation?
Re: Attention at Constant Cost per Token via Symmetry-Aware Taylor Approximation
#30Earlier quoted context omitted.
Dumb question: is the quadratic time complexity for training, inference, or both?
Attention is calculated during the forward pass of the model, which happens in both inference (forward only) and training (forward & backward).